Research Article

Fractional counterpart of third order abstract Cauchy problems and maximal accretive operators

Published in: Quaestiones Mathematicae
Volume 49 , issue 6 , 2026 , pages: 757–776

DOI: 10.2989/16073606.2026.2620620

Author(s): Mohammed Benharrat Ecole Nationale Polytechnique d’Oran-Maurice Audin (Ex. ENSET d’Oran), Algérie , Flank D.M. Bezerra Universidade Federal da Paraíba, Brazil

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Abstract

In this paper we explore the theory of fractional powers of maximal accretive operators to obtain results of existence, regularity and behavior asymptotic of solutions for linear abstract evolution equations of third order in time. An explicit representation formula of the solution is also given.

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